1. Macroeconomics - Barro Chapter 13
Taxes
Macroeconomics - Barro Chapter 13

2. Taxes in the United States
Macroeconomics - Barro Chapter 13

3. Macroeconomics - Barro Chapter 13
Types of Taxes
Macroeconomics - Barro Chapter 13

4. Macroeconomics - Barro Chapter 13
Types of Taxes
Macroeconomics - Barro Chapter 13

5. Macroeconomics - Barro Chapter 13
Types of Taxes
taxes fall on forms of income: individual income taxes, corporate profits taxes, and contributions for Social Security and Medicare.
Other taxes are based on expenditures: sales taxes, excise taxes, and customs duties.
Macroeconomics - Barro Chapter 13

6. Macroeconomics - Barro Chapter 13
Types of Taxes
The marginal tax rate is the additional tax paid on an additional dollar of income. The average tax rate is the ratio of total taxes paid to total income.
An important property of the U.S. federal individual income tax is that the marginal tax rate rises with income.
Macroeconomics - Barro Chapter 13

7. Macroeconomics - Barro Chapter 13
Types of Taxes
Macroeconomics - Barro Chapter 13

8. Macroeconomics - Barro Chapter 13
Types of Taxes
Macroeconomics - Barro Chapter 13

9. Macroeconomics - Barro Chapter 13
Types of Taxes
Macroeconomics - Barro Chapter 13

10. Macroeconomics - Barro Chapter 13
Taxes in the Model
Household Budget Constraint
C + ( 1/P)·B+ K
= ( w/P)·Ls+ r·(B/P+K) + V − T
Let τw be the marginal tax rate on labor income.
a higher τw will generate more tax revenue for the government unless the amount of labor income falls sharply.
Macroeconomics - Barro Chapter 13

11. Macroeconomics - Barro Chapter 13
Taxes in the Model
Let τw be the marginal tax rate on labor income.
a higher τw will generate more tax revenue for the government unless the amount of labor income falls sharply.
after-tax real wage rate, = (1−τw)·(w/P)
Macroeconomics - Barro Chapter 13

12. Macroeconomics - Barro Chapter 13
Taxes in the Model
If the marginal tax rate, τw, rises, for a given w/P, (1−τw)·(w/P) falls.
We predict that the household would reduce the quantity of labor supplied, take more leisure time, and consume less.
Macroeconomics - Barro Chapter 13

13. Macroeconomics - Barro Chapter 13
Taxes in the Model
V − T = −G.
Therefore, if government purchases, G, are unchanged real transfers net of real taxes, V − T, must also be unchanged. For given G, we do not get any changes in household real income through the term V − T.
In other words, if G is fixed, there are no income effects from a change in τw.
Macroeconomics - Barro Chapter 13

14. Macroeconomics - Barro Chapter 13
Taxes in the Model
Macroeconomics - Barro Chapter 13

15. Macroeconomics - Barro Chapter 13
Taxes in the Model
For a given pretax real wage rate, w/P, a higher τw implies a lower after-tax real wage rate, (1 − τw) · (w/P) .
A rise in τw shifts the labor supply curve leftward from the blue one labeled Ls to the green one labeled (Ls ) .
This decrease in labor supply reflects the substitution effect from the higher labor-income tax rate, τw
Macroeconomics - Barro Chapter 13

16. Macroeconomics - Barro Chapter 13
Taxes in the Model
a higher marginal tax rate on labor income, τw, lowers the quantity of labor input, L. This effect will spill over to the market for capital services because the reduction in L tends to reduce the marginal product of capital services, MPK.
Macroeconomics - Barro Chapter 13

17. Macroeconomics - Barro Chapter 13
Taxes in the Model
Macroeconomics - Barro Chapter 13

18. Macroeconomics - Barro Chapter 13
Taxes in the Model
Y= A· F(κ K, L)
we found that a rise in the labor-income tax rate, τw, reduced the quantities of labor, L, and capital services, κK.
A higher marginal tax rate on labor income, τw, leads to a reduction in overall market activity, as gauged by real GDP, Y.
Macroeconomics - Barro Chapter 13

19. Macroeconomics - Barro Chapter 13
Taxes in the Model
A Tax on Asset Income
C+ ( 1/P)·B+ K
= ( w/P) ·Ls+ r · ( B/P +K) + V − T
Suppose now that real taxes, T, depend on a household’s real asset income, r · (B/P + K)
r = ( R/ P) · κ − δ(κ)
Let τr be the marginal tax rate on asset income.
Macroeconomics - Barro Chapter 13

20. Macroeconomics - Barro Chapter 13
Taxes in the Model
A Tax on Asset Income
For the choice between C1 and C2 is the after-tax real interest rate, (1 τr)·r . If τr rises, for given r, (1− τr)·r declines.
Households have less incentive to defer consumption, and it reacts by increasing C1 compared to C2. For given real income in year 1, an increase in τr motivates the household to consume more and save less in year 1.
Macroeconomics - Barro Chapter 13

21. Macroeconomics - Barro Chapter 13
Taxes in the Model
A Tax on Asset Income
(1−τr) · r = (1−τr)·[(R/P)·κ−δ(κ) ]
Macroeconomics - Barro Chapter 13

22. An Increase in Government Purchases Financed by a Labor Income Tax
We know that a decrease in (1 − τr ) · r has intertemporal-substitution effects on consumption.
The household raises year 1’s consumption, C1, compared to year 2’s, C2.
For given real income in year 1, the household consumes more and saves less in year 1. That year 1’s real GDP, Y1, does not change, and that Y1 = C1 + I1 + G1. We are assuming that government purchases, G1, are unchanged.
The increase in C1 must correspond to an equal-sized reduction in year 1’s gross investment, I1.
Thus, the key result is that a higher tax rate, τr , on asset income leads to higher C1 and lower I1.
Macroeconomics - Barro Chapter 13

23. An Increase in Government Purchases Financed by a Labor Income Tax
Effects from a permanent increase in government purchases, G. assumed, that the increase in G was financed by lump-sum taxes.
Our finding was that an increase in G by one unit left real GDP, Y, unchanged and reduced consumption, C, by about one unit.
Gross investment, I, was unchanged.
Also unchanged were the real wage rate, w/P, the real rental price, R/P, and the real interest rate, r.
Macroeconomics - Barro Chapter 13

24. An Increase in Government Purchases Financed by a Labor Income Tax
We will get different results if the combination of permanently increased government purchases, G, and the higher marginal income tax rate, τw, affects the quantity of labor supplied, Ls.
Macroeconomics - Barro Chapter 13

25. An Increase in Government Purchases Financed by a Labor Income Tax
the various forces that affect Ls.
an increase by one unit in each year’s government purchases, G, required real taxes less real transfers, T − V, to rise by one unit in each year.
We found in this chapter that the substitution effect from a higher marginal tax rate, τw, on labor income reduces the quantity of labor supplied.
Macroeconomics - Barro Chapter 13

26. An Increase in Government Purchases Financed by a Labor Income Tax
Macroeconomics - Barro Chapter 13

27. An Increase in Government Purchases Financed by a Labor Income Tax
We see that the overall effect from a rise in government purchases, G, on the quantity of labor supplied, Ls, depends on the offsetting influences from an income effect and a substitution effect. The income effect predicts that Ls would rise. The substitution effect predicts that Ls would fall. The overall effect on Ls is uncertain.
Macroeconomics - Barro Chapter 13

28. An Increase in Government Purchases Financed by a Labor Income Tax
Empirically, the overall effect from permanently increased government purchases, G, on the quantity of labor supplied, Ls , seems to be small.
Macroeconomics - Barro Chapter 13

29. Macroeconomics - Barro Chapter 13
Transfer Payments
Suppose that the government increases real transfers, V, and finances these expenditures with increased real taxes, T, collected by a tax on labor income.
In this case, marginal income tax rates, τw, rise for two reasons.
First, the rise in T goes along with a higher τw for households that pay individual income taxes.
Second, for households that are receiving transfers—such as poor welfare recipients—the expansion of the transfer program raises the implicit marginal income tax rate, τw, because of the income testing for benefits.
We therefore predict even stronger effects In particular, labor input, L, capital services, κK, and real GDP, Y, tend to decline.
Macroeconomics - Barro Chapter 13